518 research outputs found
Particles and fields in fluid turbulence
The understanding of fluid turbulence has considerably progressed in recent
years. The application of the methods of statistical mechanics to the
description of the motion of fluid particles, i.e. to the Lagrangian dynamics,
has led to a new quantitative theory of intermittency in turbulent transport.
The first analytical description of anomalous scaling laws in turbulence has
been obtained. The underlying physical mechanism reveals the role of
statistical integrals of motion in non-equilibrium systems. For turbulent
transport, the statistical conservation laws are hidden in the evolution of
groups of fluid particles and arise from the competition between the expansion
of a group and the change of its geometry. By breaking the scale-invariance
symmetry, the statistically conserved quantities lead to the observed anomalous
scaling of transported fields. Lagrangian methods also shed new light on some
practical issues, such as mixing and turbulent magnetic dynamo.Comment: 165 pages, review article for Rev. Mod. Phy
Transition to Chaos in a Shell Model of Turbulence
We study a shell model for the energy cascade in three dimensional turbulence
at varying the coefficients of the non-linear terms in such a way that the
fundamental symmetries of Navier-Stokes are conserved. When a control parameter
related to the strength of backward energy transfer is enough small,
the dynamical system has a stable fixed point corresponding to the Kolmogorov
scaling. This point becomes unstable at where a stable
limit cycle appears via a Hopf bifurcation. By using the bi-orthogonal
decomposition, the transition to chaos is shown to follow the Ruelle-Takens
scenario. For the dynamical evolution is intermittent
with a positive Lyapunov exponent. In this regime, there exists a strange
attractor which remains close to the Kolmogorov (now unstable) fixed point, and
a local scaling invariance which can be described via a intermittent
one-dimensional map.Comment: 16 pages, Tex, 20 figures available as hard cop
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